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AN EXPERIMENTAL EVALUATION OF WIND TUNNEL WALL CORRECTION
METHODS FOR HELICOPTER PERFORMANCE
Hans-Juergen Langer
Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V.Institut für Flugmechanik
Braunschweig, Germany
Randall L. Peterson Thomas H. Maier
NASA Ames Research Center Aeroflightdynamics Directorate
Moffett Field, CA Aviation Research, Development and Engineering Center
U.S. Army Aviation and Troop Command
Ames Research Center
Moffett Field, CA
ABSTRACT
Accurate measurements of rotorcraft performance as
measured in a wind tunnel are strongly influenced by the
test section configuration, whether it be closed or open
jet. The influence of wind tunnel walls on the induced
velocity of lifting bodies has been studied by many
researchers over the years. Methods have been developed
to adjust the angle-of-attack and dynamic pressure for fixed
wing aircraft in a wind tunnel to approximate free flight
conditions. These methods have largely been adopted by
the rotorcraft community with very little testing to verify
the applicability of these methods to helicopter rotors andflight test measurements. Recent tests conducted by the
Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V.
(DLR) in the Duits-Nederlandse Wind Tunnel (DNW)
have provided data suitable for the evaluation of these
methods. A 40% scale model Bo105 rotor was tested in
five different wind tunnel test sections: 1) 6x6m closed, 2)
8x6m closed, 3) 8x6m open slots, 4) 9.5x9.5m closed,
and 5) the 8x6m open jet. These data along with full-scale
data from a NASA Ames 40- by 80-Foot Wind Tunnel
test and a DLR flight test program provide a means to
evaluate wind tunnel wall correction methods specifically
for helicopter rotors. Good correlation of rotor power over
a range of advance ratios for these three data sets has been
shown using wall correction methods after accounting for
trim deficiencies between the data sets.
Presented at the American Helicopter Society 52nd Annual
Forum, Washington, D.C., June 4-6, 1996. Copyright ©
1996 by the American Helicopter Society, Inc. All rights
reserved.
NOMENCLATURE
a two-dimensional lift-curve slope
A area, m2
c blade chord, m
cL non-dimensional lift coefficient, wind
axis
cP, CP non-dimensional rotor power coefficient
cT non-dimensional thrust coefficient, shaft
axis
C rotor control vector
D rotor diameter, m
D derivative matrix
F correction factor, Eq. (5)
FX x-force, N
FZ z-force, N
F hub load vector (e.g., FX ….... MZ)
L lift, N
MX rolling moment, Nm
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MY pitching moment, Nm
MZ yaw moment or torque, Nm
p per rev
R rotor radius, m
s rotor model-scale factor ( = 2.456)
T thrust, N
vtip rotor blade tip speed, m/s
V tunnel speed or flight speed, m/s
W test section width, m
∆cP0
profile power loss
∆cd 0
profile drag loss
∆α rotor correction angle due to wall
interference, rad or deg
αs, αshaft rotor mast incidence, deg
δW wall or boundary correction factor
θ0.7 collective pitch angle, r/R = 0.7
θc lateral cyclic pitch angle
θs longitudinal cyclic pitch angle
µ advance ratio, V/vtip
ρ air density, Ns2 /m4
σ solidity
Abbreviations, Superscripts and Subscripts:
FS full-scale
FT flight test or free flight
Fus fuselage
mo model rotor
Re Reynolds number
Ro rotor
TPP tip-path-plane
TS test section
WT wind tunnel
INTRODUCTION
The use of wind tunnel test measurements, flight test
measurements, and analytical prediction plays a key role
in the development of new rotor systems. Such tests are
typically performed using a range of rotor system sizes
and wind tunnel test facilities. To assure the accuracy of
wind tunnel testing methodology, a validation study is in
progress using test results from model- and full-scale tests
in comparison with flight test data. This study is being
conducted under the auspices of the U.S. Army/German
Memorandum of Understanding on Cooperative Researchin the Field of Helicopter Aeromechanics. This
comparison will allow for a determination of the ability
to accurately predict helicopter flight behavior from wind
tunnel experiments and the influence of the test facility on
these results. Experimental data from a series of wind
tunnel tests, including both model- and full-scale
experiments, have been studied to determine the extent to
which wind tunnel test results can be used to predict flight
behavior.
This paper presents the results of a recently
completed model-scale test of a Bo105 hingeless rotor in
the DNW. A 40% scale model Bo105 rotor (R = 2.0m)
was tested in five different test sections of the DNW wind
tunnel with the intent to evaluate and identify the
influence of wind tunnel walls on measured rotor
performance. The five different wind tunnel test sections
used in this series of tests included the: 1) 6x6m closed,
2) 8x6m closed, 3) 8x6m open slots, 4) 9.5x9.5m closed,
and 5) the 8x6m open jet. The influence of wind tunnel
walls and the flow breakdown phenomenon has been
studied and reported by many researchers over the years
(Refs. 1-13). From these studies, a number of methods
have been developed to account for tunnel wall induced
effects in order to approximate free-flight conditions in thewind tunnel. Results from the DNW model-scale test were
used to evaluate the applicability of two of these methods
as they apply to rotorcraft testing. Additionally, the DNW
data are compared with full-scale (R = 4.912m) data from
a NASA Ames 40- by 80-Foot Wind Tunnel test (Ref.
14) and a DLR flight test program (Ref. 15) to further
evaluate the wind tunnel wall correction methods.
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a) flight test
b) full-scale rotor
c) model-scale rotor
Figure 1. Test programs; a) flight test of Bo105
Helicopter b) full-scale tests in the 40- by 80-Foot Wind
Tunnel and c) model-scale tests in the DNW.
TEST PROGRAM
Many wind tunnel tests are conducted with scaled
models with the intention of determining the
characteristics of full-scale flight aircraft. This is done to
reduce costs and to obtain experimental measurements
within a reasonable amount of time. There is, however, agreat leap between a small-scale wind tunnel test and a
full-scale flying vehicle. Differences in structure, rotor
trim, rotor/body interaction, and the like may cause the
scale model test to not be representative of the full-scale
aircraft. Investigations into improving wind tunnel testing
methodologies and evaluation of the suitability of scaled
model testing to determine full-scale flight characteristics
are the main goals for the rotor data correlation task
within the Memorandum of Understanding (MOU)
between U.S. Army/NASA and the Institute of Flight
Mechanics of "Deutsche Forschungsanstalt für Luft- und
Raumfahrt" (DLR). Correlation efforts have been
conducted, based on flight tests, NASA Ames 40- by 80-Foot Wind Tunnel tests with a full-scale Bo105 rotor and
a test program with a scaled Bo105 rotor/fuselage in the
German-Dutch wind tunnel (DNW). Representative
photos of each of the test programs are shown in Fig. 1.
Flight Test Program
The primary task of the flight test program was to
provide the basis for follow-on wind tunnel tests of a full-
scale rotor in the NASA Ames 40- by 80-Foot Wind
Tunnel and a model-scale rotor in the German-Dutch wind
tunnel. For the data correlation task, flight data acquired at
a density altitude of approximately 762 m (2500 ft) was
used. Steady-state flights were performed between hover
and the maximum speed of the helicopter, with a stepsize
in speed of approximately 10 knots.
The primary task of the test pilot was to establish a
steady-state condition with minimum climb/descent,
sideslip or pitch rate for each forward speed. Once the
pilot was 'on condition' data was acquired with hands off
the controls. Unfortunately, when gathering data with the
pilots hands off the controls the aircraft maintains a steady
level flight condition for a very short period of time due
to the aircraft's instability. For this reason only the firstthree rotor revolutions were processed to form the flight
test database. Each speed sweep was repeated three times
to assess data scatter.
Rotor thrust could not be measured directly in the
flight test program, therefore, the aircraft weight was used
as an approximate measure. Weight was also not a direct
measure, therefore the helicopter was weighed before and
after each flight, and it was assumed that fuel
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consumption was linear with time as shown in Fig. 2. To
minimize the influence of this approximation on aircraft
weight, the flight tests were performed as quickly as
possible. It was found from the analysis of the data that
the flight test data presented in this paper is valid for a
cT = 0.005 ± 0.0001.
Since the data correlation program in the various
wind tunnels is primarily based on flight test data,
emphasis was placed on the creation of a reliable data
base. This data base consists of different sensors signals,
some of which are used just to confirm the validity of
other sensors. For example, the rotor mast torque was
used to determine rotor power, while the power indication
from the cockpit was used to check the mast torque as
shown in Fig. 3.
100
150
200
250
300
350
400
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
R e m a i n i n g F u e l , k g
Stopwatch (decimal), 24 Hours = 1.00 unit
maximum fuel (main tank) 382 kg
all values fromcockpit indicator
Figure 2. Flight test fuel consumption as a function of
time.
200
250
300
350
400
450
500
550
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Rotor MastTotal (cockpit)
P o w e r , k W
Advance Ratio, µ
Figure 3. Accuracy check of rotor mast power sensor
using the total power indicator from cockpit.
The total power data shown in Fig. 3 includes the tail
rotor power, the gearbox efficiency, and the generator
power. The power measurements shown in Fig. 3 in the
low speed region, for µ < 0.1, suggest that the speed
indicator does not provide an accurate measure in this
region. Both measures of power track with one another
well, but the curve with speed is not smooth. In this lowspeed region the airspeed sensor is probably adversely
influenced by the rotor downwash.
-12
-10
-8
-6
-4
-2
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35
R o t
o r S h a f t A n g l e , d e g
Advance Ratio, µ
Figure 4. Shaft angle versus advance ratio for three test
runs at constant density altitude.
-2000
-1000
0
1000
2000
3000
0.05 0.10 0.15 0.20 0.25 0.30 0.35
1 p S h a f t B e n d i n g M o m e n t , N m
Advance Ratio, µ
1p Cosine
1p Sine
Figure 5. Mast bending moment versus advance ratio for three test runs at constant density altitude. The 1p cosine
moment is the pitching moment and the 1p sine moment
is the rolling moment.
Other important sensors for the correlation of flight
and wind tunnel data are the rotor shaft angle (or fuselage
attitude) and the mast bending. Figure 4 shows the shaft
angle measurement versus advance ratio for three different
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speed sweeps. Repeatability of the shaft angle
measurement as compared with the least-squares curve-fit
shows acceptable data scatter. Hub pitch and roll moments
were determined from the rotating shaft bending gauges. A
once per revolution spike over the tail of the aircraft
provided a phase reference. The shaft bending moments
were harmonically analyzed and the 1p cosine and 1p sinevalues were taken as the steady pitch and steady roll
moments, respectively. These measurements may be seen
in Fig. 5 for three speed sweeps. Again, the repeatability
is acceptable.
Figures 4-5 provided the basis for trim settings in the
wind tunnel test programs in the NASA Ames 40- by 80-
Foot Wind Tunnel and in the DNW.
Other important parameters that were measured
include rotor rpm, temperature, and pressure. In addition, a
single blade was highly instrumented with 16 strain
gauges. The flapwise strain gauges, 11 in all, provide ameans to assess the elastic bending portion of the rotor
tip path-plane. The large number of sensors along the
blade span allows for the determination of the higher blade
bending modes and allows for the evaluation of the
location and number of sensors necessary to find these
modes. The rotor was also instrumented with four lead-lag
and one torsion sensor.
NASA Ames 40- by 80-Foot Wind Tunnel
Tests
From the results of the flight test program, wind
tunnel tests were conducted in the NASA Ames 40- by
80-Foot Wind Tunnel test section with a full-scale Bo105
Rotor installed on the NASA Ames Rotor Test Apparatus
(RTA) as shown in Fig. 1b. Reference 15 describes this
test program and presents the correlation of these results
with flight test.
The RTA is a special-purpose drive and support
system for operating helicopter rotors in the 40- by 80-
and 80- by 120-Foot Wind Tunnels. The RTA houses two
electric drive motors, the hydraulic servo-actuators of the
primary control-system, and a dynamic control system
capable of introducing dynamic perturbations to the non-rotating swashplate (collective and tilt) at frequencies up
to 40 Hz. Installed on the RTA is a five-component
steady/dynamic rotor balance to determine rotor loads at
the hub moment center. The balance was designed and
fabricated to measure both the steady and vibratory rotor
normal, axial and side forces, together with rotor pitching
and rolling moments up to rotor thrust levels of 98,000 N
(22,000 lb). An instrumented flex-coupling measures
rotor torque and the residual normal force.
Instrumentation for the 40- by 80-Foot Wind Tunnel
test included the five-component rotor balance and
instrumented flex-coupling, thirty-seven blade bending and
torsional moment strain gauge measurements (distributed
amongst the four blades), one rotating pitch-link
measurement, one blade root pitch angle measurement,
three stationary control system measurements and standardwind tunnel operating condition measurements.
German-Dutch Wind Tunnel (DNW) Tests
The wind tunnel test program in the DNW was
performed with the DLR's Modular Wind tunnel Model
(MWM). Reference 16 describes the capabilities of the
MWM in detail.
The complete wind tunnel model consisted of a 40%
scaled rotor and fuselage. Although a tail rotor was not
installed, the drag of the tail rotor hub and shaft were
roughly simulated by a simple cylinder. Both the rotorand the fuselage were each equipped with a 6-component
balance. Rotor torque was measured by a torque meter and
by the rotor balance. Since the rotor model allowed for the
measurement of mast bending in the rotating axis frame
and the rolling and pitching moment in the fixed axis
frame, correlation between these signals was important.
Therefore, one requirement of the test program in the
DNW had been to trim the rotor to the 1p mast moments
(sine and cosine) and to the steady rotor balance roll and
pitch moments. The influence on rotor performance (i.e.,
lift, drag and power) was not significant for these different
trim procedures.
The rotor blades were equipped with flap, lead-lag,
and torsion sensors as shown in Table 1.
Table 1. Model-scale rotor blade instrumentation.
Blade No. Flap Lag Torsion
reference 14 12 8
2 2 1 -
3 4 2 1
4 4 2 1
The wind tunnel program in the DNW was tailored to
five different tasks:
1) Correlation with flight and 40- by 80-Foot Wind
Tunnel tests;
Sections tested: 6x6m closed, 8x6m closed, 8x6m
open, 9.5x9.5m closed
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2) Rotor trim to power from flight test;
Sections tested: 6x6m closed, 8x6m closed, 8x6m
12% slotted, 8x6m open, 9.5x9.5m closed
3) Minimized flap bending moment trim for zero αshaft,
correlation with 40- by 80-Foot Wind Tunnel tests;
Sections tested: 6x6m closed, 8x6m closed, 8x6m
12% slotted, 8x6m open, 9.5x9.5m closed
4) Hover tests, correlation with flight tests and 40- by
80-Foot Wind Tunnel tests;
Sections tested: 6x6m closed, 8x6m closed, 8x6m
open
5) Derivatives, correlation with 40- by 80-Foot Wind
Tunnel tests;
Sections tested: 6x6m closed, 8x6m closed, 8x6m
open, 9.5x9.5m closed (one speed only )
Tests with minimized flap bending trim at zero shaft
angle (task 3) were conducted to identify trim differences
between the RTA in the Ames 40- by 80-Foot Wind
Tunnel test section and the scaled model in the DNW.
Since the model control is well defined, data correlation
between both configurations requires no interpolation.
The hover tests (task 4) were performed at -20° rotor
shaft angle in the closed test sections and at 0° in the open
test section.
The derivative measurements in task 5 are an
essential tool if interpolation is necessary between
measured results. Since the derivative elements (e.g.,
∆cT / ∆α) are assumed to be linear in a small α-range only,
the use of derivatives for extrapolation is often not
accurate enough.
The most important parameters (e.g., thrust, rotor
speed, etc.) were controlled in non-dimensional form so
that the density influence was considered.
In all but the open test section, DNW personnel
acquired wall pressure measurements using 92 pressure
sensors. The sensors were installed along the floor (3
rows), along the side walls (2 rows each), and along the
ceiling (3 rows). Preliminary signal analysis of the
pressure sensors shows that the flow has strong gradients
and has no symmetry. An in-depth signal analysis has not
been performed yet.
CORRECTION METHODS
From early rotor investigations in wind tunnels it is
known that wind tunnel measurements cannot directly be
applied to free-flight conditions. Rotor reactions in the
wind tunnel depend on various parameters such as:
• type of the test section (open, closed, slotted or
closed on bottom only)
• shape of the test section (rectangular, square, elliptic,
etc.)
• dimensions of the wind tunnel test section with
respect to the rotor size
• position of the model rotor regarding distance to the
wall (eccentricity)
• rotor disk loading, dynamic pressure, and wake skewangle
Additionally, the effects of tunnel blockage due to the
rotor and support system and flow breakdown due to the
impingement of the rotor downwash on the tunnel floor
in the low speed regime also affect rotor loads and
performance (e.g., power) as can be seen in Figs. 6-7.
0.00000
0.00010
0.00020
0.00030
0.00040
0.00050
0.00060
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted40x80ft
R o t o r P o w e r C o e f f i c i e n t ,
C P
Rotor Thrust Coefficient, CT
Figure 6. Rotor power as a function of rotor thrust with
smooth flow conditions, µ = 0.07, α s = 0° .
Figure 6 shows a clear difference in rotor power
between the open and closed test sections where smooth
flow in the tunnel exists. This difference becomes small
or even vanishes for conditions where flow breakdown
exists as shown in Fig. 7. Therefore, wall correction
methods are not applicable for conditions of flow
breakdown.
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0.00010
0.00020
0.00030
0.00040
0.00050
0.00060
0.00070
0.00080
0.00090
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted40x80ft
R o t o r P o w e r C o
e f f i c i e n t , C P
Rotor Thrust Coefficient, CT
Figure 7. Rotor power as a function of rotor thrust with
flow breakdown conditions, µ = 0.023, α s = 0° .
Corrections For Wall Interference
Wind tunnel wall induced interference can partly be
eliminated by applying angle-of-attack corrections to the
rotor shaft. Open test sections also require corrections, but
of opposite sign to that of closed test sections.
To determine the direction of the angle-of-attack
correction, one must imagine that the rotor flow is
deflected by the test section ceiling which sharply turns
the inflow. The test section floor changes the direction of
the downwash, while the side walls have an impact on the
rotation of the rotor flow. All can influence the local
angle-of-attack due to inflow along the blade span.
Due to the change in inflow caused by the test
section ceiling the rotor needs a more negative incidence
to compensate for this effect. This is opposite to that for
an open test section.
Glauert Correction Methodology
Glauert was the first to investigate in detail wind
tunnel wall induced effects on wings. The Glauert
correction is considered to be the classical or conventional
wall correction method for fixed wing testing in a windtunnel. The average downwash or induced angle correction
is in the form
∆α =
δw Awing
ATS
cL
(1)
where Awing is the wing area, ATS is the test section area
and δW is the boundary correction factor. The boundary
correction factor, δW is dependent on the test section
shape, the ratio of the wing span to tunnel width and the
position of the wing in the test section. A comprehensive
collection of boundary correction factors for various test
section shapes can be found in Ref. 2.
Assuming lift Lwing is equivalent to the rotor thrust
T, but
Lwing = ƒ(V) and T = ƒ(vtip),
cL of Eq. (1) can be replaced by cT using
cL
≡ cT
vtip
2
V2
(2)
With
µ =V
vtip
Eq. (1) becomes
∆α =
2 δw cT
Aro
µ2 A
TS
180π [deg] (3)
and
∆α = αFT
− αWT
(4)
Note that Eq. (3) has a factor of 2 due to the fact that δWfor wings refers to the wing span and thus 2R for rotors.
The boundary correction factors used in this paper are
found in Table 2. Also shown in Table 2 are the
corresponding values for rotor diameter to wind tunnel test
section width. The boundary correction factors for the
DNW test sections were determined from the figures foundin Ref. 2. The boundary correction factor for the 40- by
80-Foot Wind Tunnel was determined from a figure found
in Ref. 17.
In addition, δW can also be found by using more
comprehensive flow correction theories or by experiment
as will be discussed later.
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Table 2. Wall correction factors δW from Ref. 2 and 17.
Test Section D/W δW
DNW 6x6m closed 0.667 0.160
DNW 8x6m closed 0.500 0.119
DNW 9.5x9.5m closed 0.421 0.145DNW 8x6m open 0.500 -0.158
Ames 40x80ft 0.403 0.112
For completeness it should be mentioned that a
similar closed form equation can be found in Ref. 10 as
shown below
∆α = F tan-1
(
cT
cos αFT
2 µ
2
- cT sin αFT
) (5)
Without substantial lack on accuracy the above
equation can be re-written
∆α = F
cT
2 µ2
(6)
The factor 2 in Eq. (6) comes from the air density
that is often given as ρ instead of ρ /2 when thrust is
written in the non-dimensional form.
From Eqs. (3) and (6) one gets the correction factor F
F = 4 δw Aro
ATS
(7)
Heyson and Brooks Correction Methodologies
To determine boundary correction factors (δW) or for
local angle-of-attack corrections along the blade span,Heyson's approach is widely used. The Heyson approach
is based on 'potential theory' assumptions (Refs. 3-6).
This method can be applied to rectangular test sections
that can be closed, open, or closed on the bottom only.
The resulting angle-of-attack and dynamic pressure
corrections are dependent on various parameters such as
rotor to test section width, width to height ratio, tunnel
speed, rotor radius, hub eccentricity, rotor rotational speed
and thrust. The FORTRAN programs of Heyson are found
in Ref. 4.
When a disagreement was found between calculated
correction factors as determined by the Langley modified
version of the Heyson program, and the boundary
correction factors found in Ref. 2, it was determined thatthe Langley version contained a coding error. As a result
of this disagreement and the desire to determine a detail
mapping of wind tunnel corrections over the region of the
rotor disk, Brooks derived a new correction method (Refs.
12-13). Results from this code have been validated by
comparing correction values with those from a variety of
published benchmark correction cases.
The approach used by Brooks is similar to that used
by Heyson, however it is based on vortical rather than
dipole wake distribution modeling. The Brooks code
contains streamline curvature effects due to a lifting rotor
in rectangular test sections. This code gives a spatialdistribution of the correction, while the Heyson code
gives only the correction in the rotor disk plane. Solid and
wake blockage effects are not included in the Brooks code
since it is assumed that in an open test section the stream
is free to expand and in a closed test section the model
size is much smaller than the cross-sectional area.
The Brooks code has been applied to all DNW test
sections with the exception of the slotted walls. Because
this paper deals only with rotor performance rather than
local blade loads, results from Brooks code are used solely
for the calculation of the global angle-of-attack correction,
∆α. Angle-of-attack corrections (∆α's) as calculated by
the Brooks code are compared with the ∆α's from Eq. (3)
and δW 's from Table 2. Comparisons of the Glauert
equation results with the results from the Brooks code are
shown in Figs. 8-10. More detailed comparisons of each
method are presented in the results section of the paper.
Figure 8 is a comparison of the angle-of-attack
corrections for the Glauert equation and the Brooks code
calculations as a function of rotor thrust at a fixed advance
ratio (µ = 0.072). For the 6x6m closed test section, the
Glauert equation calculates a larger ∆α-correction as a
function of rotor thrust than the Brooks code calculations.Also, the difference in the ∆α-corrections between the two
methods increases with increasing thrust. Figure 9 is a
comparison of the angle-of-attack corrections as a function
of advance ratio for the 6x6m closed test section. The
calculations shown in Fig. 9 are for a fixed value of rotor
thrust (cT = 0.005). The difference in the ∆α-corrections
between the two methods is greatest at the lowest speeds
and the difference decreases as advance ratio is increased.
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2
3
4
5
6
7
8
9
0.002 0.003 0.004 0.005 0.006 0.007 0.008
Brooks Codeδw = 0.16, Ref. 2
A n g l e - O f - A t t a c k C o
r r e c t i o n ∆ α , d e g
Rotor Thrust Coefficient, CT
Figure 8. Correction angles as a function of rotor thrust
from the Brooks code and Eq. (3), µ = 0.072, 6x6m closed
test section.
0
1
2
3
4
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Brooks Codeδw = 0.16, Ref. 2
A n g l e - O f - A t t a c k C o r r e c t i o n ∆ α , d e g
Advance Ratio, µ
Figure 9. Correction angles as a function of advance ratio
from the Brooks code and Eq. (3), cT = 0.005, 6x6m
closed test section.
Figure 10 is a comparison of the angle-of-attack
corrections as a function of advance ratio for the 8x6m
closed test section. The calculations shown in Fig. 10 are
for a fixed value of rotor thrust (cT = 0.005) similar to
those shown in Fig. 9. Unlike Fig. 9, the difference in
the ∆α-corrections between the two methods is negligibleover the whole speed range.
Figures 8-10 show that there can be differences in the
calculated ∆α-corrections between the Glauert formula and
the Brooks code. At this point it is not known which
method is more accurate. It may be that the boundary
correction factor, δW for the 6x6m closed test section has
to be re-determined. A new value for δW can be
determined by feeding the ∆α value from the Brooks code
into Eq. (3) as will be discussed in the next section of the
paper.
0
1
2
3
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Brooks Codeδw = 0.119, Ref. 2
A n g l e - O f - A t t a c k C o r r e c t i o n ∆ α
, d e g
Advance Ratio, µ
Figure 10. Correction angles as a function of advance
ratio from the Brooks code and Eq. (3), cT = 0.005, 8x6m
closed test section.
Correction Factors Derived From The Brooks
Code
The Brooks code ∆α-results were fed back into Eq.
(3) resulting in new boundary correction factors, δW as
given in Table 3. The boundary correction factors in Table
3 can be applied to all cT's and all µ's. This is important
to know because it allows on-line global angle-of-attack
correction within a test program. Using δW from Table 3,
the differences between ∆α from the Brooks code and the
Glauert formula are negligible. Also shown in Table 3 are
the corresponding values for rotor diameter to wind tunnel
test section width.
Table 3. Boundary correction factors (δW) as determined
by the Brooks code.
Test Section D/W δW
DNW 6x6m closed 0.667 0.1353
DNW 8x6m closed 0.500 0.1163
DNW 9.5x9.5m closed 0.421 0.1345DNW 8x6m open 0.500 -0.1775
DNW 8x6m 12% slotted* 0.500 -0.0081
*δW determined from experiment
The boundary correction factor for the open test
section given in Table 3 is related to an 8x6m effective
test section size. Due to flow contraction, the effective
tunnel dimensions may be somewhat smaller (e.g.,
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7x5m). An exact value can hardly be given as it depends
on the rotor condition (e.g., thrust) and its position with
respect to the tunnel flow.
The wall correction factor for the 8x6m slotted wall
test section is of high interest as it indicates that this test
section needs only negligible ∆α-corrections for rotortesting. This has been confirmed by fixed wing
measurements. In addition, fixed wing measurements have
indicated that α-corrections are necessary along the
longitudinal axis of the model in the flow direction due to
a longitudinal velocity gradient (Ref. 7). The negative
sign of boundary correction factor (δW) shows that the
slotted test section behaves more like an open section
than a closed section.
Although the Brooks code is not applicable for the
8x6m slotted wall configuration, the boundary correction
factor can be determined based on the measured results
from the other test sections. Since it will be shown in asubsequent section of the paper that corrections for
different test sections will collapse the power data onto a
single curve, one can use this data to extrapolate to a test
section that cannot be represented by the Brooks code if
one assumes that these corrections are accurate. From the
power difference between the corrected and uncorrected data
one can determine the ∆α, and thus the δW with the help
of Eq. (3). Strictly speaking, this procedure may only be
used for identical test configurations.
Correction By Experiment
A prerequisite for the application of this method is
that data from flight tests (e.g., rotor power and shaft
angle) or from calculations are available and reliable. An
applicable procedure is to trim the rotor in the wind
tunnel to the measured rotor power from flight test by
adjusting the shaft angle while maintaining constant cL.
This is the so-called trim to torque method (TtoT). This
method allows for the determination of the difference
between αFT and αWT and thus the angle-of-attack
correction (∆α) due to wall interference, assuming all
other differences (i.e., scale, inflow, Reynolds No., ...) are
negligible. The TtoT procedure is described in more detail
in a later section of the paper.
Figures 11-13 show the variation in rotor power as a
function of rotor shaft angle (αshaft) for three different
advance ratios. A dashed horizontal and vertical line
represent the regression curve-fits of the rotor mast power
and the flight test shaft angle (see also Fig. 4). The
intersection between the rotor shaft angle in the wind
tunnel and power from flight test is the corresponding
free-flight condition. These figures show that with
0.00025
0.00030
0.00035
0.00040
0.00045
-25 -20 -15 -10 -5 0 5 10 15
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted
R o t o r P o w e r C o
e f f i c i e n t , C P
Rotor Shaft Angle, deg
From Flight TestRegression Curves
Figure 11. Rotor shaft power versus rotor shaft angle,
µ = 0.056, c L = cweight = 0.005.
0.00020
0.00022
0.00024
0.00026
0.00028
0.00030
-7 -6 -5 -4 -3 -2
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted
R o t o r P o w e r C o e f f i c i e n t , C P
Rotor Shaft Angle, deg
From Flight TestRegression Curves
Figure 12. Rotor shaft power versus rotor shaft angle,
µ = 0.172, c L = cweight = 0.005.
0.00040
0.00045
0.00050
0.00055
-11 -10 -9 -8 -7
8x6m open8x6m closed6x6m closed
R o t o r P o w
e r C o e f f i c i e n t , C P
Rotor Shaft Angle, deg
From Flight TestRegression Curves
Figure 13. Rotor shaft power versus rotor shaft angle,
µ = 0.32, c L = cweight = 0.005.
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increasing speed, the shaft angle difference between the
intersection of the linear curve-fits and the flight test
regression curve data becomes smaller between the
different test sections. This is consistent with the wall
correction theories where the wall induced angle-of-attack
corrections reduce with increasing advance ratio, µ.
Corrections For Scaling Effects
Rotor loads and performance testing at model-scale
requires careful design and manufacturing to simulate full-
scale rotor behavior. In particular, the tip Mach number
must be very close or equal to that of the full-scale rotor
to capture the influence of compressibility on blade
section loading. Blade per rev natural frequencies and Lock
number must also be very close to provide similar coning
and flapping. However, the Reynolds number for the scale
model rotor will not match the full-scale values unless the
model is run at higher pressures, either in a pressurized
tunnel or by changing the working fluid of the tunnel.
Table 4. Comparison of full-scale (flight and wind tunnel)
and model-scale rotors.
model Bo105 Factor*
Rotor Diameter [m] 4.0 9.82 s-1
Rotor Speed [rpm] 1040 424 s
Blade Chord [m] 0.121 0.27 0.91s
Blade Twist [deg] -8 -8 1
Tip Speed [m/s] 218 218 1
Solidity, σ 0.077 0.07 0.91s
Hub Precone Angle [deg] 2.5 2.5 1
Tip Mach No. 0.64 0.64 1
Re-No. at r/R = 0.7, x10-6 1.26 2.82 2.24
Blade Profile NACA 23012 mod.
*Scale Factor s = 2.456
The 40% scale model Bo105 rotor tested in air at the
DNW was designed according to the criteria stated above.
Following conventional Mach scaling rules with both
rotors running at a tip Mach number of 0.64, the full-scale and model-scale Reynolds numbers at 70% radius are
2.82 and 1.13 million respectively. Wind tunnel
measurements conducted by Messerschmitt-Bölkow-
Blohm GmbH (MBB) on a NACA 23012 airfoil have
shown that this reduction in Reynolds number causes a
decrease in cL,max from 1.58 to 1.35, or about 15%, and a
decrease in the lift-curve slope of about 7.5%. Therefore,
the airloads for the model blade would be low with respect
to the inertial and elastic forces when compared to the
full-scale rotor. To compensate for this relative decrease in
airloads at model-scale, the blade chord was increased by
10%. The influence of this increase in the model-scale
chord is assessed below. Important rotor parameters and
the resulting scale factors for the full-scale and model-
scale rotors are given in Table 4. The influence of
Reynolds number on rotor performance for model-scalerotor testing was addressed in Ref. 18. In Ref. 18 it was
shown that the non-dimensional power consumption for a
conventionally Mach scaled model rotor was higher than a
full-scale rotor under the same conditions. From Ref. 18,
∆cP
0
= cP
0,FS
- cP
0,mo
(8)
∆cP0
=
σ ∆cd
0
8 (1+ 4.6 µ
2) (9)
cd
0,FS
cd
0,mo
= ( ReFS
Remo)
5
(10)
Since Remo < ReFS and from Eq. (10) is
cd
0,mo
> cd
0,FS
From (8) and (9)
∆cd
0
< 0 and ∆cp0
< 0
Therefore
cP
O,FS
< cP
O,mo
This was shown in Ref. 18, as an offset in the power
coefficient versus thrust coefficient curves for a full-scale
and a one-sixth scale CH-47D rotor in hover. A similar
comparison for the rotors discussed here shows no offset
in the power coefficient versus thrust coefficient curves
between the full-scale Bo105 and the 40% scale model
Bo105 with 10% increase in chord length. This may be
seen in Fig. 14, where the full-scale rotor was tested in
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the NASA Ames 40- by 80-Foot Wind Tunnel and the
scale model rotor was tested in the DNW 8x6m open jet
test section at the same tip Mach number. The good
agreement in hover performance between the full- and
model-scale rotors indicate that the increase in chord
length for the model-scale rotor was an effective means of
compensating for the Reynolds number difference,although differences due to profile roughness,
compressibility effects, and the body or test stand were
not investigated.
0.00000
0.00020
0.00040
0.00060
0.00080
0.000 0.002 0.004 0.006 0.008
8x6m open40x80ft
R o t o r P o w
e r C o e f f i c i e n t , C P
Rotor Thrust Coefficient, CT
Figure 14. Comparison of full- and model-scale rotor
power as a function of rotor thrust in hover.
ROTOR TRIM PROCEDURES
The goals of the 40% scale model DNW test were to
measure rotor performance and blade loads on a model-
scale rotor for the same conditions as were measured on a
flight vehicle by the DLR, and to assess the wall
corrections of the different test sections used at the DNW.
To acquire wind tunnel data suitable for the first goal one
must determine what is required to establish the same
condition in the wind tunnel that existed for a particular
flight point. Several different methods of adjusting the
rotor control to achieve comparable trim conditions with
the flight data were investigated.
During the full-scale Bo105 rotor test in the 40- by80-Foot Wind Tunnel, three different trim conditions were
established to compare with flight; minimized flapping
trim, prescribed hub moment trim, and prescribed cyclic
control angle trim (Ref. 15). All of these methods had in
common the same rotor speed, shaft angle, rotor thrust,
and tunnel speed. The prescribed hub moment trim
requires the rotor operator to adjust the cyclic stick control
until the steady hub pitch and roll moments agree with
values measured from the flight aircraft. Minimized
flapping trim requires the rotor operator to adjust the
cyclic stick control until the 1p flap moment in the
flexure portion of the blade is a minimum (i.e., near
zero). Cyclic control angle trim requires the rotor operator
to adjust the cyclic stick control until the longitudinal and
lateral cyclic displays agree with values that were
measured on the flight aircraft. These different trimprocedures cause the rotor tip-path-plane to deviate from
one another resulting in different hub loads. Ideally, the
prescribed hub moment trim and cyclic control angle trim
methods would result in very similar conditions, however,
the measurements shown in Ref. 15 show that the
resulting hub loads were very different. Hub loads for
minimized flapping trim were expected to be different
from the other two trim procedures and this was the case.
0.00020
0.00024
0.00028
0.00032
0.10 0.15 0.20 0.25 0.30
HM trim; 8x6m closedMF trim; 8x6m closedHM trim; 8x6m openMF trim; 8x6m open
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 15. Comparison of rotor power as a function of advance ratio for minimized flapping (MF) and hub
moment (HM) trim, cT = 0.005.
Prescribed hub moment and minimized flapping trim
were again used in the model-scale DNW test. Figure 15
compares the rotor power coefficient versus advance ratio
for these two trim methods in the 8x6m closed and 8x6m
open jet test sections in the DNW. Both the trim method
and the test section are seen to have a strong influence on
the rotor power. This shows the importance of choosing
an accurate trim procedure. It further shows the
significance of the test section used in the wind tunnel anddemonstrates that some type of correction is required. The
large differences shown in Fig. 15 along with the
comparison with flight data shown in Ref. 15 indicate
that minimized flapping trim is not suitable for
comparisons with flight data. It does, however, provide a
well-defined condition that will certainly be used in wind
tunnel testing for a long time. The cyclic control angle
trim has been investigated by the DLR and NASA and
was found to produce large differences in hub loads when
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compared to flight data, so it was not used in the DNW
test.
The experimental test set-up in the DNW allowed
additional methods of achieving the flight trim conditions.
Because the rotor and the model-scale fuselage were
mounted independently of each other on their own balancemeasuring device, the rotor and fuselage forces and
moments could be measured independently. Independent
measurements of rotor lift and fuselage lift provided the
capability to trim the rotor lift to match the sum of the
flight aircraft weight and the vertical force on the fuselage
as defined by Eq. (11).
- cWeight = cL,Ro + cL,Fus = cL (11)
This method removes the inaccuracy of assuming that
rotor thrust is equal to aircraft weight, which is often used
because cL,Ro and cL,Fus from flight are normally not
known. At low speed the rotor induces a download on thefuselage producing a negative value of cL,Fus and at high
speed the fuselage aerodynamics are likely to produce
significant negative value of cL,Fus. Trimming to lift as
described above, assumes instead that the rotor wake and
the model-scale fuselage behave in a similar manner
aerodynamically to the flight aircraft.
Until now it had been assumed that the shaft angle
measured in flight was accurate enough to establish
comparable flight test trim conditions in the wind tunnel.
Figure 15 clearly indicates that there is a significant
influence on rotor power due to the wind tunnel test
section. Therefore, a means of correcting for wall effects
is required. An alternative approach to achieving the rotor
trim of flight was evaluated for the first time in the
DNW. The rotor was trimmed to rotor speed, rotor lift
coefficient as defined by Eq. (11), tunnel speed, and hub
pitch and roll moment coefficient. However, instead of
trimming to the flight shaft angles, the shaft angle was
adjusted until the measured shaft torque coefficient agreed
with the flight measurement. Results for this trim to
torque method (TtoT) are shown in Figs. 11-13. Since
flight test data normally show a certain amount of scatter,
three shaft angles were tested which bracket the flight
power coefficient. From these tests, linear relationships of the change in the rotor power coefficient as a function of
rotor shaft angle was established at each forward speed
tested. These relationships and how they were used are
discussed in a subsequent section of the paper.
Another approach to acquiring relationships similar
to the trim to torque method, is to acquire data with small
positive and negative perturbations in all the trim controls
(e.g., V, α, θ0.7 , θc, θs) around a baseline condition.
This derivative approach provides the information to
correct the measured performance data for any parameter
that turns out to be off the target trim value. However, it
does require a significant investment in tunnel occupancy
time to gather all the necessary derivatives. For the DNW
test, the derivatives were taken after trimming to rotor
speed, shaft angle, rotor thrust coefficient, tunnel speed,and hub pitch and roll moment coefficient. The results are
more or less linear relationships between the control
vector elements and the hub load vectors.
Since only the differences are of interest one can write
∆F = D * ∆C ,
where each element of matrix D gives the slope of load
vector F and control vector C.
The differences between the closed and open testsection are clearly seen in the derivative data. The
derivatives appear linear with advance ratio within the
scatter of the data.
Representative results are shown in Figs. 16-18,
where the change in thrust due to the change in three
control vector elements are shown.
The derivative method is more general than the trim
to torque method and was therefore applied for angle-of-
attack corrections within the minimized flapping, zero
shaft tilt test series. This will be shown in a later section
of the paper.
600
700
800
900
1000
1100
0.10 0.15 0.20 0.25 0.30
8x6m closed8x6m open6x6m closed
∆
F z /
∆ θ 0 . 7 , N / d e g
Advance Ratio, µ
Figure 16. Collective derivative as a function of advance
ratio for the 40% scale model rotor, hub moment trim.
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0
100
200
300
400
500
0.10 0.15 0.20 0.25 0.30
8x6m closed8x6m open6x6m closed
∆ F z / ∆ θ s ,
N / d e g
Advance Ratio, µ
Figure 17. Longitudinal cyclic derivative as a function of
advance ratio for the 40% scale model rotor, hub moment
trim.
50
100
150
200
250
300
350
400
450
0.10 0.15 0.20 0.25 0.30
8x6m closed8x6m open6x6m closed
∆ F z / ∆ α s , N / d e g
Advance Ratio, µ
Figure 18. Shaft angle derivative as a function of advance
ratio for the 40% scale model rotor, hub moment trim.
RESULTS
Trim Comparisons
Once the trim procedure has been established,
experimental consideration determines whether thesetargets are simultaneously achieved. In this section, the
ability to match hub moments and a comparison of the
resulting 1p blade flapping moments are shown. The
flight test trim target was established as steady level flight
with minimum sideslip and no control input during data
gathering. Steady hub moments were derived from
harmonic analysis of the strain gauge signals on the
rotating shaft.
In the last section several wind tunnel trim procedures
were described. For the data shown in this section a single
trim procedure was used for each wind tunnel. The full-
scale test in the 40- by 80- Foot Wind Tunnel defined
trim as matching rotor speed, shaft angle, tunnel velocity,
rotor thrust equal to aircraft weight, hub pitch moment,
and hub roll moment matching flight measurements. Thehub moments were derived from balance measurements
made below the rotor hub yet transferred to the hub center.
The 40% scale-model test in the DNW defined trim as
matching rotor speed, shaft angle, tunnel velocity, rotor
lift equal to the sum of the aircraft weight and the vertical
force on the scale model fuselage, 1p cosine shaft
bending, and 1p sine shaft bending matching flight
measurements.
-2000
-1500
-1000
-500
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test40x80ftDNW, all TS
R o l l i n g M o m e n t , N m
Advance Ratio, µ
Figure 19. Comparison of measured hub roll moment as a function of advance ratio, c L = 0.005.
0
500
1000
1500
2000
2500
3000
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test40x80ftDNW, all TS
P i t c
h i n g M o m e n t , N m
Advance Ratio, µ
Figure 20. Comparison of measured hub pitch moment as
a function of advance ratio, c L = 0.005.
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-300
-200
-100
0
100
0.0 0.2 0.4 0.6 0.8 1.0
Flight Test40x80ft8x6m closed
1 p C o s i n e B l a d e F l a p M o m e n t , N
m
Blade Span r/R
Figure 21. Longitudinal 1p flap moment distribution
versus span, c L = 0.005, µ = 0.32.
-100
-50
0
50
100
150
0.0 0.2 0.4 0.6 0.8 1.0
Flight Test40x80ft8x6m closed
1 p S i n e B l a d e F l a p M o m e n t , N m
Blade Span r/R
Figure 22. Lateral 1p flap moment distribution versus
span, c L = 0.005, µ = 0.32.
The ability to match the flight test targets may be
seen in Figs. 19-20, where the 40% scale model rotor data
have been scaled up for comparison. Figure 19 compares
the rolling moment for these three tests. The flight data
show relatively little scatter except at low forward speed
where the speed indication is least accurate. In general the
correlation is good. Figure 20 compares the pitchingmoment for these three tests. The pitching moment is of
particular interest because it has a direct influence on the
longitudinal tip-path-plane tilt, and since typical wind
tunnel wall corrections impose an angle-of-attack
correction, factors affecting tip-path-plane angle-of-attack
are clearly important. Flight data shows more scatter for
pitch moment than was seen for roll moment. This is
most likely due to basic aircraft stability, atmospheric
unsteadiness, and slight deviations from steady level flight
equilibrium. The 40- by 80- Foot Wind Tunnel data is
slightly off the flight test target values at low speed and
more significantly for the highest speed point where
unsteadiness in the tunnel flow made it difficult to
maintain a steady hub pitching moment. Unfortunately,
there was only time for a single data point at each speed.It is expected that had more time been made available for
gathering this data the agreement with pitch moments
would be better.
Another way to assess the ability to which wind
tunnel trim agrees with flight trim is to look at the
resulting flapping moment along the span of the blades.
Figure 21 shows the cosine component of the 1p flapping
moment for the comparable highest speed points. The
moment distributions look very similar except in the root
section for the 40- by 80- Foot Wind Tunnel data. There
are two things that can possibly explain this difference.
Blade-to-blade dissimilarities as was shown in Ref. 15 canbe one explanation for these differences. The other
explanation to these differences is that the pitch moment
does not agree well with the flight target value at this
speed. Figure 22 shows the sine component of the 1p
flapping moment with span for the comparable highest
speed points. Better agreement is seen here over the entire
span due to the good agreement in hub roll moments.
Wall Induced Corrections
The primary focus of this paper is the presentation of
the results from a series of systematic tests conducted in
the DNW to identify the influence of tunnel walls on
measured rotor performance and to evaluate the ability of
existing wall correction methodologies to minimize
facility dependent effects. To quantify the influence on the
measured rotor performance of the various DNW test
section configurations, two different approaches for rotor
trim were used throughout this test program. Minimized
flap bending moment trim was used to investigate the
influence of wall induced effects on measured rotor
performance as a function of rotor thrust and advance
ratio. Prescribed hub moment trim, where the cyclic
controls were adjusted until rotor hub moments matched
values measured during previous flight testing were usedto make comparisons with free-flight rotor performance in
addition to investigating wall induced effects.
To quantify the influence of the tunnel walls on the
measured rotor performance both as a function of forward
speed and rotor thrust, a series of thrust sweeps utilizing a
minimized flap moment trim was conducted at discrete
forward speeds in each of the five different test section
configurations. Due to forward speed limitations in some
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0.00010
0.00015
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.002 0.003 0.004 0.005 0.006 0.007 0.008
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted
R o t o r P o w e r C o e f f i c i e n t , C P
Rotor Thrust Coefficient, CT
Figure 23. Comparison of rotor power as a function of
rotor thrust for five different DNW test sections,
minimized flap bending trim,µ = 0.106, α s = 0° .
0.00010
0.00015
0.00020
0.00025
0.00030
0.002 0.003 0.004 0.005 0.006 0.007 0.008
8x6m open8x6m closed6x6m closed
R o t o r P o w e r C o e f f i c i e n t , C P
Rotor Thrust Coefficient, CT
Figure 24. Comparison of rotor power as a function of
rotor thrust for three different DNW test sections,
minimized flap bending trim,µ = 0.251, α s = 0° .
of the test section configurations, not all test conditions
were repeated. The influence of the tunnel test section on
rotor power with minimized flap moment trim is clearly
seen in Figs. 23-24. Figure 23 shows the rotor power as a
function of rotor thrust at low speed (µ = 0.106) for the
five different test section configurations. Figure 24 shows
the rotor power as a function of rotor thrust at high speed(µ = 0.251) for the three test sections for which data is
available. The data presented in Figs. 23-24 have not been
corrected for the wall induced effects. The data shown in
these two figures quantify the influence of the test section
size on rotor power as measured in this test program. The
trends with rotor thrust are very clear in both of these
figures. The data demonstrate that the influence of the
tunnel walls increases as rotor thrust increases. It also
shows that the measured power is lower with relatively
smaller test sections. Both of these findings are consistent
with existing wind tunnel wall correction methodologies.
Differences between the 6x6m and the 8x6m closed test
sections are much greater in Fig. 23 at low speed thanthey are in Fig. 24 at high speed. This trend is also
consistent with existing wall correction theories.
The influence of the wall induced effects on rotor
power as a function of tunnel speed is more clearly seen
in Fig. 25. This figure shows rotor power as a function of
tunnel speed with rotor thrust and hub moments adjusted
to match flight test measurements. Data is presented for
five different test section configurations. The data
presented in Fig. 25 has not been corrected for the wall
induced effects. The influence of the tunnel walls reduces
as the tunnel speed increases. This is consistent with the
measurements shown in Figs. 23-24 for minimized flapmoment trim. These uncorrected measured data using
prescribed hub moment trim in the different test sections
will be referred to as 'baseline' measurements.
Measurements with corrections for the influence of the
tunnel walls or corrections to provide equivalent trim
conditions will be compared to these baseline
measurements.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.05 0.10 0.15 0.20 0.25 0.30 0.35
9.5x9.5m closed8x6m open8x6m closed6x6m closed8x6m 12% slotted
R o t o r P o w e r C o e f f i c i e n t ,
C P
Advance Ratio, µ
Figure 25. Comparison of rotor power as a function of
advance ratio without wall corrections for five different DNW test sections with identical rotor trim conditions.
To quantify the influence of the tunnel walls on the
measured rotor performance and to evaluate the existing
wall correction methodologies upon completion of the
DNW test program, a series of tests (trim to torque) was
developed and utilized in each of the test section
configurations. To allow for interpolation of the change
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-10
-5
0
5
10
0.05 0.10 0.15 0.20 0.25 0.30 0.35
8x6m open, BaselineBrooks CodeGlauert Eq.
R o t o r S h a f t A n g l e , d e g
Advance Ratio, µ
Figure 26. Comparison of baseline and wall corrected rotor
shaft angle as a function of advance ratio in the 8x6m
open jet test section.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.05 0.10 0.15 0.20 0.25 0.30 0.35
8x6m open, BaselineBrooks CodeGlauert Eq.
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 27. Comparison of baseline and wall corrected rotor
power coefficient as a function of advance ratio in the
8x6m open jet test section.
in rotor power as a function of rotor shaft angle, the rotor
was trimmed with rotor thrust and hub moments adjusted
to match flight test measurements at several rotor shaft
angles around the measured flight test shaft angle. From
these tests, a linear relationship of the change in the rotor
power coefficient as a function of rotor shaft angle was
established at each forward speed tested.
Two wall correction methodologies were selected for
evaluation. The wall correction methodologies selected are
the classical wall-correction method of Glauert (Glauert
Eq.) and the Brooks computer code (Brooks Code). These
methods are presented and discussed in a previous section
of the paper. The results of these evaluations are presented
in Figs. 26-31.
Comparison of baseline and corrected rotor shaft
angle and rotor power coefficient data as a result of the
two wall correction methodologies for the 8x6m open jettest section are shown in Figs. 26-27. Figure 26 presents
a comparison of the wall corrected shaft angles (includes
∆α-correction) with the baseline shaft angle as a function
of advance ratio for the two wall correction
methodologies. The rotor shaft angle requirements as
determined by the Glauert equation and the Brooks
computer code are very similar. For advance ratios greater
than 0.15, the shaft angles are essentially identical. Small
differences (less than one deg) in rotor shaft angle
requirements were determined for advance ratios less than
0.15. The corresponding comparison of rotor power
coefficient for each of the correction methodologies with
the baseline as a function of advance ratio is shown inFig. 27. Using the ∆α-correction's from Fig. 26, both
methodologies result in nearly the same rotor power over
the entire speed range with negligible differences at the
lowest speeds.
Results for the 8x6m closed test section are shown in
Figs. 28-29. Comparisons of the baseline wind tunnel
shaft angle as a function of advance ratio with the wall
corrected shaft angles are shown in Fig. 28. The Glauert
equation and the Brooks computer code calculate nearly
identical values for shaft angle over the entire speed range.
Comparisons of the corresponding rotor power
coefficients with advance ratio are shown in Fig. 29.
Based on the nearly identical corrected shaft angle results
shown in Fig. 28, it is not surprising that the rotor power
is nearly identical over the entire speed range as shown in
Fig. 29.
Comparison of the results for each of the four test
sections using the same correction methodology in each is
shown in Figs. 30-31. Results using the Brooks
computer code correction method are shown in Fig. 30.
Figure 31 presents the results for each test section using
the Glauert equation correction method. The results for the
8x6m open and closed test sections shown in Figs. 30-31are the same as those presented in Figs. 26-29 comparing
the different correction methodologies in each test section.
Although direct comparisons of the two correction
methodologies for the 9.5x9.5m and 6x6m closed test
sections are not shown in the paper, the shaft angle and
rotor power coefficient results were found to be very
similar to those shown in Figs. 26-29.
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-10
-8
-6
-4
-2
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35
8x6m closed, BaselineBrooks CodeGlauert Eq.
R o t o r S h a f t A
n g l e , d e g
Advance Ratio, µ
Figure 28. Comparison of baseline and wall corrected rotor
shaft angle as a function of advance ratio in the 8x6m
closed test section.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.05 0.10 0.15 0.20 0.25 0.30 0.35
8x6m closed, BaselineBrooks CodeGlauert Eq.
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 29. Comparison of baseline and wall corrected rotor
power coefficient as a function of advance ratio in the
8x6m closed test section.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.05 0.10 0.15 0.20 0.25 0.30 0.35
9.5x9.5m closed8x6m open8x6m closed6x6m closed
R o t o r P o w e r C o
e f f i c i e n t , C P
Advance Ratio, µ
Figure 30. Comparison of wall corrected rotor power
coefficient as a function of advance ratio using the Brooks
code correction in four different DNW test sections.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.05 0.10 0.15 0.20 0.25 0.30 0.35
9.5x9.5m closed8x6m open8x6m closed6x6m closed
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 31. Comparison of wall corrected rotor power
coefficient as a function of advance ratio using the Glauert
equation correction in four different DNW test sections.
Results using the Brooks code are shown in Fig. 30
for each of the test sections. As seen in Fig. 30, the
corrections based on the Brooks computer code have
collapsed the data from the 9.5x9.5m, 8x6m and 6x6m
closed test sections onto a single curve. For comparisonpurposes, refer to Fig. 25 that shows the uncorrected data
and the distinct differences in the measured rotor power for
each test section. The results for the 8x6m open jet test
section indicate that perhaps not enough correction was
made to this set of data relative to the other three test
sections. Further review of this data set indicated that the
resultant propulsive force was greater in the 8x6m open
jet test sect ion than the other test sections despite
attempts to maintain consistent test conditions
throughout. The greater propulsive force in the 8x6m
open jet test section resulted in higher measured rotor
power.
The results of corrected rotor power using the Glauertequation correction method for each of the test sections are
compared in Fig. 31. The comparisons shown in Fig. 31
are very similar to those shown in Fig. 30. This is to be
expected based on the comparisons of correction
methodologies shown previously where the Brooks
computer code calculations and the Glauert equation
corrections were nearly the same. As seen in Fig. 31, the
Glauert equation correction has collapsed the data from the
9.5x9.5m, 8x6m and 6x6m closed test sections onto the
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same curve. The results for the 8x6m open jet test section
are very similar to that shown in Fig. 30 as is to be
expected based on the comparisons shown in Fig. 27.
Propulsive Force Trim
The testing approach used to account for wall inducedcorrections as discussed in the previous section also
resulted in linear relationships identifying the change in
propulsive force with rotor shaft angle at each of the
forward speeds tested. These relationships were determined
so that a consistent propulsive force equilibrium for the
rotor could be maintained during the evaluation of each of
the wall correction methodologies. These relationships
were used to correct the baseline values from each of the
DNW test sections to the correct propulsive force
representing the equivalent flat plate area of the Bo105
helicopter and subsequently the influence of the tunnel
walls as defined by an angle-of-attack correction from each
of the wall correction methodologies under evaluation.For the Bo105 helicopter (including rotor hub and shaft),
the equivalent flat plate area is 1.33 m2 (14.32 ft2) as
provided by Eurocopter Deutschland (ECD).
0
1
2
3
4
5
0.05 0.10 0.15 0.20 0.25 0.30 0.35
9.5x9.5 closed8x6 open8x6 closed6x6 closed
E q u i v a l e n t F l a t P l a t e A r e a , m 2
Advance Ratio, µ
1.33 m2
Figure 32. Comparison of equivalent flat plate areas as
measured in each of the four DNW test sections with the
ECD provided value of 1.33 m2.
Figure 32 presents a comparison of the equivalent flatplate areas as determined from data measured in each of the
four DNW test sections as a result of trim conditions
based on the shaft angle measurements from flight test
and Eq. (11). Also shown on this figure is a horizontal
reference line representing the equivalent flat plate area
value of 1.33 m2 as provided by ECD. For all advance
ratios greater than 0.10, the equivalent flat plate area as
determined in the wind tunnel is less than this value. The
differences identified in this figure are the basis for the
propulsive force correction to the wind tunnel data using
the linear relationships of the change in power and
propulsive force with rotor shaft angle.
The first step in the analysis of this data was to
correct the baseline wind tunnel data from each of the
DNW test sections, in this case the rotor propulsive forceto that which is determined by the equivalent flat plate
area. By moving up or down the linear relationship of
propulsive force as a function of rotor shaft angle at each
forward speed, a corrected value of rotor shaft angle was
established by matching the propulsive force to the
prescribed flat plate area of 1.33 m2. This corrected value
for rotor shaft angle primarily addresses the uncertainty
and scatter of the flight test measurements. The other
uncertainty that is not addressed directly in this analysis is
the uncertainty in the measurement of the aircraft speed.
-12
-10
-8
-6
-4
-2
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35
8x6m closed, Baseline
8x6m closed, Propulsive Force Trim
R o t o r S h a f t A n g l e , d e g
Advance Ratio, µ
Figure 33. Comparison of baseline shaft angle with shaft
angle for propulsive force trim in the wind tunnel as a
function of advance ratio.
Figure 33 shows a representative comparison of the
baseline wind tunnel rotor shaft angle (without wall
induced corrections) as determined from flight test with
the rotor shaft angle due to propulsive force corrections of
the wind tunnel data as a function of advance ratio. This
corrected rotor shaft angle value at each forward speed was
then used to determine the corrected rotor powercoefficient using the linear relationship of the change in
rotor power coefficient as a function of rotor shaft angle.
A comparison of corrected rotor power coefficient based
on propulsive force trim (without wall induced
corrections) with measured rotor power in the 8x6m
closed test section based on rotor shaft angle from flight
test as a function of advance ratio is shown in Fig. 34.
Also shown on Fig. 34 is the measured rotor power data
from flight test for three different speed sweeps as
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discussed previously in this paper. The importance of
propulsive force trim corrections to the measured wind
tunnel data is evident in Fig. 34 at the higher advance
ratios. Evaluations with different equivalent flat plate
areas were also conducted. From these evaluations it
appears that the value provided by ECD was indeed the
most appropriate or representative value for thesecomparisons.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test8x6m closed, Baseline8x6m closed, Propulsive Force Trim
R o
t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 34. Comparison of baseline and propulsive force
trim corrected rotor power coefficient in the wind tunnel
as a function of advance ratio with flight test
measurements.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.00060
0.05 0.10 0.15 0.20 0.25 0.30 0.35
PFT ReferenceBrooks Code
Glauert Eq.
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 35. Comparison of propulsive force trim (PFT)
reference and wall corrected rotor power coefficient as a
function of advance ratio in the 8x6m open jet test
section.
Results using the propulsive force trim analysis with
and without wall corrections applied for the 8x6m open
and closed test sections are shown in Figs. 35-36. Figure
37 compares the four different DNW test sections using
the Brooks computer code correction method. All data
presented have been corrected to an equivalent flat plate
area of 1.33 m2 (14.32 ft2) before application of
corrections for wall induced effects.
Comparison of propulsive force trim reference andcorrected rotor power coefficient data as a result of the two
wall correction methodologies for the 8x6m open jet test
section is shown in Fig. 35. This figure may be compared
with Fig. 27 to show that propulsive force trim has little
influence on the final corrected rotor power coefficient
results for µ < 0.25. However, the wind tunnel wall
corrected rotor power coefficient result for propulsive force
trim is 15% greater at µ = 0.32. As is to be expected from
the results previously shown in Fig. 27, the corrected
rotor power coefficients for the Glauert equation and the
Brooks computer code methodologies are nearly identical.
Rotor power coefficient results for the 8x6m closedtest section are shown in Fig. 36. Comparison of the
propulsive force trim reference rotor power coefficient
with the corrected rotor power coefficients based on the
two wall correction methodologies as a function of
advance ratio as shown in Fig. 36 is very similar to that
shown in Fig. 29. As was shown in Fig. 29 and again in
Fig. 36, the results using either wall correction method
are virtually identical.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.00060
0.05 0.10 0.15 0.20 0.25 0.30 0.35
PFT ReferenceBrooks CodeGlauert Eq.
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 36. Comparison of propulsive force trim (PFT)reference and wall corrected rotor power coefficient as a
function of advance ratio in the 8x6m closed test section.
Comparisons of the propulsive trim results for each
of the four test sections using the Brooks computer code
calculations are shown in Fig. 37. The comparisons are
very similar to those shown in Fig. 30, except that the
results for the 8x6m open jet test section have collapsed
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onto essentially the same curve as that for the 8x6m and
6x6m closed test sections at the higher speeds. This
improvement is largely due to the requirement for
longitudinal force equilibrium between different test
section data sets. At low speeds there still remain some
differences as the influence of propulsive force on rotor
power is small or negligible up to advance ratios of 0.15as shown in Fig. 34. Remaining differences, although
small, may indicate that not enough correction was
identified by the correction methodology or there may be
accuracy and repeatability limitations within the different
data sets that has not yet been identified.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.00060
0.05 0.10 0.15 0.20 0.25 0.30 0.35
9.5x9.5m closed8x6m open8x6m closed6x6m closed
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 37. Comparison of wall corrected rotor power
coefficient as a function of advance ratio using the Brooks
code correction in four different DNW test sections,
propulsive force trim.
Model-Scale/Full-Scale Flight Correlation
In addition to the test series developed to evaluate
existing wall correction methodologies, another series of
tests was conducted for direct comparison with data
acquired in the NASA Ames Research Center 40- by 80-
Foot Wind Tunnel. These data points were acquired, for
the most part, at speeds other than those described in the
previous series of tests and did not include variations in
rotor shaft angle about a baseline value to determine the
rotor power coefficient and propulsive force relationships.To apply the rotor power coefficient and propulsive force
corrections to these data, relationships of the change in
rotor power coefficient and propulsive force with rotor
shaft angle as a function of advance ratio were determined.
The relationships of rotor power coefficient and
propulsive force with rotor shaft angle as functions of
rotor thrust and advance ratio for the full-scale 40- by 80-
Foot Wind Tunnel were determined from the
comprehensive data base reported in Ref. 14. These
relationships were then used to correct the corresponding
data for wall induced effects so that direct comparisons of
model- and full-scale wind tunnel test and flight test data
could be made as shown in Figs. 38-40. The wind tunnel
data presented in Figs. 39-40 have been corrected to an
equivalent flat plate area of 1.33 m2 (14.32 ft2).
Model- and full-scale results with and without
corrections for propulsive force and wall induced effects
for this series of tests are presented in Figs. 38-40.
Although this series of tests was conducted in each of the
four test sections, only the results for the 8x6m closed
test section are shown for clarity. The results for the other
test sections are very similar to the results shown
previously in Figs. 26-31 and Figs. 35-37. Also shown
in Figs. 38-40 is the corresponding flight test data
previously shown in Fig. 34.
Comparisons of model- (8x6m closed) and full-scale
(40x80ft) wind tunnel data without corrections for eitherpropulsive force trim or wall induced effects are shown in
Fig. 38. Measurements of rotor power from flight are also
shown in Fig. 38. As seen in Fig. 38, the model- and
full-scale rotor power data as measured in the wind tunnel
for identical trim conditions compare reasonably well for
advance ratios greater than 0.15. It is clear from Fig. 38
that both the model- and full-scale data do not compare
well with the flight test data. Comparisons (not shown)
of the baseline equivalent flat plate areas as measured in
the wind tunnel for both the model- and full-scale rotors
were very similar to the data shown previously in Fig.
32.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test8x6m closed40x80ft
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 38. Comparison of model- and full-scale rotor
power as a function of advance ratio without propulsive
force trim or wall induced correct ions with flight test
measurements.
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Model- and full-scale results that account for the
propulsive force trim to an equivalent flat plate area of
1.33 m2 (without wall induced corrections) are shown in
Fig. 39 along with flight test measurements. Application
of propulsive force corrections improved the correlation of
the model- and full-scale wind tunnel data for advance
ratios above 0.15, along with improvements in thecorrelation with flight test. Figure 39 clearly shows the
importance of the propulsive force trim corrections in the
correlation of these wind tunnel and flight test results.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test8x6m closed40x80ft
R o t o r P o w
e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 39. Comparison of model- and full-scale rotor
power with flight test measurements as a funct ion of
advance ratio for propulsive force trim.
Rotor power results that include corrections for both
propulsive force and wall induced effects from the 8x6m
closed test section and the 40- by 80-Foot Wind Tunnel
are compared with flight test measurements in Fig. 40.
Both the model- and full-scale wind tunnel data were
corrected using the Glauert equation correction
methodology. The reason for selecting the Glauert
equation correction method is that the Brooks code
calculations are really only applicable for rectangular test
section shapes. Because the 40- by 80-Foot Wind Tunnel
is not rectangular, small errors in the analysis might be
introduced with the use of the Brooks code to determine
the angle-of-attack corrections. For advance ratios greater
than 0.20, both the model- and full-scale results comparereasonably well with flight test. At the lower speeds, the
model-scale results tend to follow more closely to the
trends of the flight test, however there is sufficient scatter
in the flight test data to be misleading in making this
statement. Difficulties in maintaining a trimmed
repeatable condition in flight at these low speeds makes it
difficult to make any definitive statements regarding the
correlation of either the model- or full-scale data with
flight test measurements. Overall, the correlation of
model- and full-scale wind tunnel test data with flight test
results is reasonably good.
0.00020
0.00025
0.00030
0.00035
0.00040
0.00045
0.00050
0.00055
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Flight Test8x6m closed, Glauert Eq.40x80ft, Glauert Eq.
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 40. Comparison of model- and full-scale rotor power as a function of advance ratio with propulsive force
trim and wall induced corrections with flight test
measurements.
One possible explanation for the differences shown in
Figs. 38-40 between the model- and full-scale results for
advance ratios less than 0.15 is that the geometry of the
two test sections is sufficiently different so as to affect the
rotor downwash at the lower speeds. The 8x6m closed test
section is a rectangular tunnel, while the 40- by 80-Foot
Wind Tunnel is a closed test section with semicircular
sides of 20 ft radius. As suggested in Ref. 9, the addition
of fillets or in this case the influence of the semicircular
sides may be reducing the allowable downwash or lift of
the rotor. This is offered only as a possible explanation
for these differences.
Model-Scale/Full-Scale Minimized Flapping
Trim Correlation
As shown in the previous section, the propulsive
force trim approach showed good correlation between
flight and wind tunnel test rotor power. It is also possible
to avoid the propulsive force issue and just look atcomparing the measured performance of the two wind
tunnel tests. Data gathered with minimized flapping trim
and αs = 0°, while not suitable for comparison with flight
test, are especially suited for wind tunnel to wind tunnel
comparisons. Figures 40-41 present a comparison
between the full-scale rotor in the Ames 40- by 80-Foot
Wind Tunnel and the 40% scaled model rotor in the
DNW. Since the rotor trim is well-defined with this
approach, results can be directly compared.
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0.00010
0.00015
0.00020
0.00025
0.00030
0.00035
0.05 0.10 0.15 0.20 0.25 0.30
8x6m closed8x6m open40x80ft
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 41. Comparison of model- and full-scale rotor
power as a function of advance ratio for minimized
flapping trim, α s = 0° , cT = 0.005.
Figure 41 shows full-scale rotor power in the 40- by
80-Foot Wind Tunnel with rotor power for the 40% scaled
model rotor in the open and closed DNW test sections.
The α TPP is held constant as a result of the trim
procedure for all advance ratios. Full- and model-scale data
for the closed test sections are very similar indicating that
the wall induced angle-of-attack corrections are of the
same magnitude. The differences between the open and
closed test sections also reduce as the tunnel speed
increases. This is consistent with the results presented
previously, indicating that the results are independent of
αTPP and in agreement with wall correction theory.
0.00010
0.00015
0.00020
0.00025
0.00030
0.00035
0.05 0.10 0.15 0.20 0.25 0.30
8x6m closed8x6 open7x5m open, effective40x80ft
R o t o r P o w e r C o e f f i c i e n t , C P
Advance Ratio, µ
Figure 42. Comparison of model- and full-scale wall
corrected rotor power as a function of advance ratio using
the derivative correction method for minimized flapping
trim, α s = 0° , cT = 0.005.
Comparison of the power curves from the 40- by 80-
Foot Wind Tunnel and the 8x6m closed test section as
shown in Fig. 41, indicate that the different model
supports (RTA and 40% model-scale fuselage on the
DNW sting) appear to have negligible influence on rotor
power.
Figure 42 presents a comparison of the wall-corrected
rotor power for the two wind tunnel tests. The angle-of-
attack corrections were determined using the Brooks code,
and the corresponding changes in power were determined
using the derivative method. Since the speed derivatives
(e.g., ∂cP / ∂V) are non-linear, the derivative method is
only accurate for speeds where derivatives were measured.
Unfortunately, the experimental derivatives were not
obtained at the advance ratio values shown in Fig. 41.
Therefore it was necessary to use the least-squares curve
fit in Fig. 41 to provide uncorrected values of rotor power
at the advance ratio values for which derivatives were
available. Linearity can be assumed for the α-derivativefor small perturbations thus providing the power
corrections required for the calculated ∆α's.
Due to the uncertainty of the effective test section
size of the 8x6m open test section (as previously
discussed), the wall induced angle-of-attack corrections
were also calculated for a 7x5m open test section. The
smaller open test section size data collapses much better
with the data from the 40- by 80-Foot Wind Tunnel and
the 8x6m closed test sections.
CONCLUDING REMARKS
The influence of wind tunnel test section physical
characteristics on measured rotor performance both as a
function of rotor thrust and advance ratio were clearly
shown.
The influence of wind tunnel wall induced interference
on performance measurements can be compensated for by
means of a global angle-of-attack correction. Both the
Glauert equation and the Brooks computer code appear to
provide adequate angle-of-attack corrections for rotor
performance.
It was shown, that with proper trim procedures (i.e.,
hub moment and propulsive force trim) and corrections for
wall induced interference effects, that it is possible to
acquire model- and full-scale performance data in the wind
tunnel that agrees well with flight measurements.
Differences in the model- and full-scale rotor supports
used in the two wind tunnel tests reported here appears to
have a negligible influence on the measured rotor power.
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At nominal thrust values with the 40% scale model
Bo105 rotor, the 8x6m slotted test section requires the
smallest angle-of-attack corrections as compared to the
other available DNW test sections.
REFERENCES
1 Glauert, H., "The Interference on the Characteristics of
an Airfoil in a Wind Tunnel of Rectangular Section," R
& M 1459, 1932.
2 Pope, Alan, and Harper, John J., Low-Speed Wind
Tunnel Testing, John Wiley & Sons, Inc., 1966.
3 Heyson, H. H., "Use of Superposition in Digital
Computers To Obtain Wind Tunnel Interference Factors
for Arbitrary Configurations, With Particular Reference to
V/STOL Models," NASA TR R-302, 1969.
4 Heyson, H. H., "FORTRAN Programs For CalculatingWind-Tunnel Boundary Interference," NASA TM X-1740,
1969.
5 Heyson, H. H., "Rapid Estimation Of Wind Tunnel
Corrections With Applications To Wind Tunnel And
Model Design," NASA TN D-6416.
6 Heyson, H. H., "Linearized Theory of Wind-Tunnel Jet-
Boundary Corrections and Ground Effect for VTOL-STOL
Aircraft," NASA TR R-124, 1962.
7 Garner, H. C., Rogers, E. W., Acum, W. E. A., and
Maskell, E. C., "Subsonic Wind Tunnel Wall
Corrections," AGARDograph 109, October 1966.
8 Rae, W. H. Jr., "Limits on Minimum-Speed V/STOL
Wind Tunnel Tests," Journal of Aircraft , Vol. 4, (3),
May-June 1967, pp. 249-254.
9 Rae, W. H. Jr., and Shindo, S., "An Experimental
Investigation of Wind Tunnel Wall Corrections and Test
Limits for V/STOL Wind-Tunnel Tests," U.S. Army
Grant No. DA-ARO-31-124-G-809, Project No. 4506-E,
AD-764 255, Dept. of Aeronautics and Astronautics,
Univ. of Washington, July 1973.
10 Brooks, T. F., Jolly, J. R., and Marcolini, M. A.,
"Helicopter Main Rotor Noise," NASA TP 2825, August
1988.
11 Shinoda, P. M., "Wall Interaction Effects For A Full-
Scale Helicopter Rotor In The NASA Ames 80- By 120-
Foot Wind Tunnel," Paper Nº 20, AGARD 73rd Fluid
Dynamics Panel Meeting and Symposium on Wall
Interference, Support Interference and Flow Field
Measurements, Brussels, Belgium, October 1993.
12 Brooks, T. F., and C. L. Burley, C. L., "A Wind
Tunnel Wall Correction Model for Helicopters in Open,
Closed, and Partially Open Rectangular Test Sections,"
NASA TM to be published August 1996.
13 Beaumier, P., Tung, C., Kube, R., Brooks, T. F. et
al., "Effect of Higher Harmonic Control on Helicopter
Rotor Blade-Vortex Interaction Noise: Prediction and
Initial Validation," AGARD Symposium on Aerodynamic
and Aeroacoustic of Rotorcraft; Berlin, Germany; October
11-13, 1994.
14 Peterson, R. L., "Full-Scale Hingeless Rotor
Performance and Loads," NASA TM 110356, June 1995.
15 Peterson, R. L., Maier, T., Langer, H. J., and
Tränapp, N., "Correlation of Wind Tunnel and Flight TestResults of a Full-Scale Hingeless Rotor," Proceedings of
the American Helicopter Society Aeromechanics
Specialist Conference, San Francisco, CA, January 1994.
16 Stephan, M., Klöppel, V., and Langer, H. -J., "A New
Test Rig For Helicopter Testing," Proceedings of the
Fourteenth European Rotorcraft Forum, Milan, Italy,
1988.
17 Johnson, W., and Silva, F., Rotor Data Reduction
System User's Manual for the National Full-Scale
Aerodynamics Complex NASA Ames Research Center,
1986.
18 Keys, C. N., Mc Veigh, M. A., Dadone, L., and Mc
Hugh, F. J., "Considerations In The Estimation Of Full-
Scale Rotor Performance From Model Rotor Test Data,"
Proceedings of the 39th Annual Forum of the American
Helicopter Society, St. Louis, MO, May 1983.